namespaceboost{namespacemath{template<classRealType=double,classPolicy=policies::policy<>>classskew_normal_distribution;typedefskew_normal_distribution<>normal;template<classRealType,classPolicy>classskew_normal_distribution{public:typedefRealTypevalue_type;typedefPolicypolicy_type;// Constructor:skew_normal_distribution(RealTypelocation=0,RealTypescale=1,RealTypeshape=0);// Accessors:RealTypelocation()const;// mean if normal.RealTypescale()const;// width, standard deviation if normal.RealTypeshape()const;// The distribution is right skewed if shape > 0 and is left skewed if shape < 0.// The distribution is normal if shape is zero.};}}// namespaces

The skew normal distribution is a variant of the most well known Gaussian
statistical distribution.

The skew normal distribution with shape zero resembles the Normal
Distribution, hence the latter can be regarded as a special case
of the more generic skew normal distribution.

The skew_normal distribution with shape = zero is implemented as a special
case, equivalent to the normal distribution in terms of the error
function, and therefore should have excellent accuracy.

The PDF and mean, variance, skewness and kurtosis are also accurately evaluated
using analytical
expressions. The CDF requires Owen's
T function that is evaluated using a Boost C++ Owens
T implementation of the algorithms of M. Patefield and D. Tandy,
Journal of Statistical Software, 5(5), 1-25 (2000); the complicated accuracy
of this function is discussed in detail at Owens
T.

The median and mode are calculated by iterative root finding, and both
will be less accurate.